The cop fired eight times, with one bullet accidentally hitting Rebello, 21, in the head, he said.

The other seven rounds struck and killed Smith, a career criminal, ex-con and parole absconder, Azzata said.

Smith — clad in dark clothes and a ski mask — was wielding a 9mm pistol with one bullet in the chamber and another in the magazine, Azzata said. But he never got off a shot during the deadly encounter early Friday inside the off-campus house in Uniondale where Rebello lived with her twin sister, Jessica, Azzata said.

The cop who fired the shots was described only as a 12-plus-year veteran of the Nassau County Police Department who earlier served more than seven years with the NYPD.

A source told The Post his decorations include the medal of honor.

He was treated for trauma after the incident, said James Carver, head of the Nassau County Patrolmen’s Benevolent Association.